I think one can take the social-construction thing too far -- way too far. It is very strange that one wing of feminism argues that gender has no physical basis, while the other wing argues that medical research must take those physical differences more into account!
If there is NO physical basis for assigning sex, how ever do parents decide whether their newborn is a son or daughter? At this point the social=constructionists tend to mention ambiguously sexed people (see? sometimes parents CAN'T tell). That there are anomalous intersexed people doesn't invalidate the basic binary model, any more than the occasional birth of a person with six fingers means people come in ten-fingered and eleven-fingered varieties.
We could conceivably have a society in which men wear skirts and makeup and most engineers are women. But I don't think we can have a society in which men are the childbearers. That makes a difference! How much difference, and what kind of difference is a social question. Up to a point. It DOESNT mean all women bear children, should bear children, aren't "real women" if they don't. It just means that ONLY women bear children. And that only one sex bears the physical costs of reproduction -- menstruation, pregnancy, childbirth, abortion, breastfeeding-- is a complex and important fact.
The fact that it took the economist transsexual 30 operations to change his/her sex--including four or five just to get rid of his/her beard! -- suggests to me not how trivial physical gender is, but how real it is! And of course, in some important ways he ISN"T a physical woman. he doesn't have xx chromosome. If he has a stroke and becomes aphasic, his ability to relearn language will be that of a man (not so good) rather than a woman (better, because of subtle differences in brain structure, language centers in both halves of the brain instead of, as with men, only one).
And sure there are women with beards and men with breasts -- but there are also furless cats and dogs that have no bark.